# Geometric Understanding of Discriminability and Transferability for Visual Domain Adaptation

arXiv: https://arxiv.org/abs/2407.09524 · HTML: https://mlsanity.com/paper/2407.09524/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 71 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [VisDA: The Visual Domain Adaptation Challenge](https://mlsanity.com/paper/1710.06924/) (2017)
- [Confidence Regularized Self-Training](https://mlsanity.com/paper/1908.09822/) (2019)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [Towards Discriminability and Diversity: Batch Nuclear-norm Maximization under Label Insufficient Situations](https://mlsanity.com/paper/2003.12237/) (2020)
- [Cycle Self-Training for Domain Adaptation](https://mlsanity.com/paper/2103.03571/) (2021)
- [Deep Subdomain Adaptation Network for Image Classification](https://mlsanity.com/paper/2106.09388/) (2021)
- [Scatter Component Analysis: A Unified Framework for Domain Adaptation and Domain Generalization](https://mlsanity.com/paper/1510.04373/) (2015)
- [ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction](https://mlsanity.com/paper/2105.10446/) (2021)
- [SENTRY: Selective Entropy Optimization via Committee Consistency for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2012.11460/) (2020)
- [Maximum Density Divergence for Domain Adaptation](https://mlsanity.com/paper/2004.12615/) (2020)
- [Discriminative Adversarial Domain Adaptation](https://mlsanity.com/paper/1911.12036/) (2019)
- [Learning Invariant Representations and Risks for Semi-supervised Domain Adaptation](https://mlsanity.com/paper/2010.04647/) (2020)
- [Adversarial-Learned Loss for Domain Adaptation](https://mlsanity.com/paper/2001.01046/) (2020)
- [Domain Invariant Representation Learning with Domain Density Transformations](https://mlsanity.com/paper/2102.05082/) (2021)
- [Dynamic Weighted Learning for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2103.13814/) (2021)
- [SphereFace2: Binary Classification is All You Need for Deep Face Recognition](https://mlsanity.com/paper/2108.01513/) (2021)

## Built on by (most cited first, 2 of 2)

- [Rethinking Time Series Domain Generalization via Structure-Stratified Calibration](https://mlsanity.com/paper/2603.02756/) (2026)
- [Reliable Neural Collapse Approximation for Open-World Test-Time Adaptation](https://mlsanity.com/paper/2608.19890/) (2026)

## Abstract (arXiv)

To overcome the restriction of identical distribution assumption, invariant representation learning for unsupervised domain adaptation (UDA) has made significant advances in computer vision and pattern recognition communities. In UDA scenario, the training and test data belong to different domains while the task model is learned to be invariant. Recently, empirical connections between transferability and discriminability have received increasing attention, which is the key to understanding the invariant representations. However, theoretical study of these abilities and in-depth analysis of the learned feature structures are unexplored yet. In this work, we systematically analyze the essentials of transferability and discriminability from the geometric perspective. Our theoretical results provide insights into understanding the co-regularization relation and prove the possibility of learning these abilities. From methodology aspect, the abilities are formulated as geometric properties between domain/cluster subspaces (i.e., orthogonality and equivalence) and characterized as the relation between the norms/ranks of multiple matrices. Two optimization-friendly learning principles are derived, which also ensure some intuitive explanations. Moreover, a feasible range for the co-regularization parameters is deduced to balance the learning of geometric structures. Based on the theoretical results, a geometry-oriented model is proposed for enhancing the transferability and discriminability via nuclear norm optimization. Extensive experiment results validate the effectiveness of the proposed model in empirical applications, and verify that the geometric abilities can be sufficiently learned in the derived feasible range.